Question

Using properties of proportion solve:
$\frac{\sqrt{3x+4}+\sqrt{3x-4}}{\sqrt{3x+4}-\sqrt{3x-5}}=9$

Answer 1

Given $\frac{\sqrt{3x+4}+\sqrt{3x-5}}{\sqrt{3x+4}-\sqrt{3x-5}}=\frac{9}{1}$

$\Rightarrow \frac{2\sqrt{3x+4}}{2\sqrt{3x-5}}=\frac{10}{8}$

$\Rightarrow \frac{\sqrt{3x+4}}{\sqrt{3x-5}}=\frac{5}{4}$

$\Rightarrow 16(3x+4)=25(3x-5)$

$\Rightarrow 48x+64=75x-125$

$\Rightarrow 189=27x$

$\Rightarrow x=\frac{189}{27}$

$\therefore x=7$